在径向磁场作用下圆柱上的自旋1/2粒子
Spin 1/2 Particle on a Cylinder with Radial Magnetic Field
摘要：
研究了径向磁场作用下，约束在圆柱表面的带电量子粒子的运动。当忽略粒子的自旋时，系统本质上简化为一个无限族的简谐振子，沿圆柱轴等距分布。有趣的是，它可以用作量子傅立叶Transformer，具有方便的视觉输出。当考虑自旋为1/2的粒子时，非常规微扰分析导致对粒子的所有本征态和所有磁矩阶的能量和波函数的递归闭合形式的校正。一个简单的两态系统，其中的时间演化涉及的自旋垂直于磁场的近似进动。一些图突出了调查结果，而几个三维动画已在网上提供。
英文摘要：
We study the motion of a charged quantum particle, constrained on the surface of a cylinder, in the presence of a radial magnetic field. When the spin of the particle is neglected, the system essentially reduces to an infinite family of simple harmonic oscillators, equally spaced along the axis of the cylinder. Interestingly enough, it can be used as a quantum Fourier transformer, with convenient visual output. When the spin 1/2 of the particle is taken into account, a non-conventional perturbative analysis results in a recursive closed form for the corrections to the energy and the wavefunction, for all eigenstates, to all orders in the magnetic moment of the particle. A simple two-state system is also presented, the time evolution of which involves an approximate precession of the spin perpendicularly to the magnetic field. A number of plots highlight the findings while several three-dimensional animations have been made available on the web.
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